There is a few addons you can use to track it yourself for example
Mount Journal Enhanced - Addons - World of Warcraft - CurseForge
Features
- Filter mounts by an extended source, color, faction, type, family or expansion
- Filter unusable or unwanted mounts
- Display mounts which are actually hidden by the game (TCG, PvP, secrets etc.)
- Sort mounts by name, type or expansion (or in reverse)
- Saves filter options
- Double click list entry to summon mount
- Compact mount list
- Move equipment slot into display to save space
Display count of character specific mounts <-------------------------- - Display mount related achievement points
- Freely rotate display camera around mount
- Trigger /mountspecial within the display
- Browse through mounts with Up/Down arrow keys
- Right Click on scroll buttons to quickly go to the top or bottom
- Track, display and sort by your usage statistics
- Favor all filtered mounts at once or unset them all
- Save favorites per character
- Auto-favor new learned mounts
- Resize the journal window
- Works with ElvUI
Helpful hint always use a paladin as main mount counter 
It should as horde and alliance do not have same amount of mounts atm.